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Questions tagged [logical-deduction]

A puzzle that requires formal logical deduction to arrive at the solution. This suggests more than merely reasoning through clues to find an answer (you might want [situation] for that).

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196 votes
26 answers
96k views

In the 100 blue eyes problem - why is the oracle necessary?

The riddle Randall Munroe (of xkcd fame) has, a bit hidden on his site, a logic puzzle: A group of people with assorted eye colors live on an island. They are all perfect logicians -- if a ...
dwjohnston's user avatar
  • 2,280
136 votes
13 answers
24k views

This is it. This is the one. Find your wife

If you have found her, maybe you could try saving her? You come home one day and find your wife is out. You open your computer and discover an email from her. To xxxxx, / Curiosity killed the ...
Beastly Gerbil's user avatar
135 votes
16 answers
1.8m views

Two doors with two guards - one lies, one tells the truth

You are a prisoner in a room with 2 doors and 2 guards. One of the doors will guide you to freedom and behind the other is a hangman–you don't know which is which, but the guards do know. One of the ...
Rafe's user avatar
  • 5,846
115 votes
2 answers
58k views

3 Logicians Walk Into a Bar

Three logicians walk into a bar. The barman says, 'Does everybody want a drink?' The first logician says, 'I don't know.' The second logician says, 'I don't know.' What does the third logician say? ...
Bob's user avatar
  • 4,273
107 votes
9 answers
21k views

Five coloured doors, which leads to freedom?

You have been incarcerated in a high-security prison for several nefarious crimes which we need not go into here. The warden, being a kindly logician, offers you a single chance to escape. You are ...
Rand al'Thor's user avatar
104 votes
15 answers
41k views

My wife has died

In 1980, a man lives on the 30th floor of his building. Every morning he wakes up, gets ready, kisses his wife, takes the elevator down to the first floor, and goes to work. One morning, he wakes ...
Aggie Kidd's user avatar
  • 11.7k
93 votes
7 answers
18k views

Thanks, dad! Never again

No idea why my dad dragged me into this place. Some guy is performing on the stage. He's reading numbers out loud. I think it's some kind of a sequence puzzle. 1... 8... 9... 16... 17... ...
Jafe's user avatar
  • 78k
88 votes
18 answers
17k views

Nine gangsters and a gold bar

One night nine gangsters stole a gold bar. When the time came for dividing the bar, they faced a problem: two of the criminals put guns to each other's faces. Now it's up to fate whether one of them ...
Glinka's user avatar
  • 1,317
84 votes
11 answers
23k views

Correct way to add 22 to 4 to get 82

Inspired by this other puzzle, tell me a correct way by which adding 22 to 4 will give 82. As in that other puzzle, these numbers are all expressed in base 10.
Trevor Powell's user avatar
84 votes
2 answers
5k views

My God, it's full of stars!

An entry in Fortnightly Topic Challenge #32: Grid Deduction Hybrids My dear friend, unknown to us, may have relocated again. He sent me imagery and constellation maps indicating that a distant red ...
paramesis's user avatar
  • 4,629
78 votes
28 answers
20k views

You have one question to tell whether the number I'm thinking of is 1, 2, or 3

This is an interesting puzzle which was passed to me by a friend some time ago. I do know the answer, but will refrain from self-answering on this to see where it goes. I'm thinking of a number: 1, 2,...
user avatar
77 votes
14 answers
16k views

Three logicians walk out of the bar

It is known that when logicians get drunk they may claim not to know the answer to a question when they should know it very well. After a night of heavy drinking at the bar, three logicians decide ...
GOTO 0's user avatar
  • 13.5k
77 votes
9 answers
17k views

Is a married person looking at an unmarried person?

I remember answering this one incorrectly and when the answer was explained to me I was annoyed with myself. Here is your chance, with the original word phrasing: Jack is looking at Anne, but Anne ...
Halvard's user avatar
  • 875
75 votes
21 answers
31k views

Are there eighteen or twenty bars in my castle?

Two friends, Mark and Rose, are very famous logicians; they are so clever that they can deduce any logic connection possible in a matter of minutes even from the most vague situation. Unfortunately, ...
Marco Bonelli's user avatar
75 votes
2 answers
7k views

Oh dang, I have to change my whole answer!

One day, you enter your math classroom. On the board, there are the words POP QUIZ. Dang it! Was it about fractions? you knew you were bad with fractions. You look down. $\begin{array}{|cc|} \...
bleh's user avatar
  • 3,625
73 votes
9 answers
512k views

Crack the lock code

Does any one know how to crack this? I got this as a challenge.
Qaisar Satti's user avatar
68 votes
2 answers
5k views

Sudoku like you've never seen it before

I've spent this week trying to create a difficult logic puzzle which is a combination of two Sudoku varaints, 'Samuari Sudokus' and 'Pseudokus', and this combo is unlike anything you can find online. ...
Beastly Gerbil's user avatar
67 votes
7 answers
12k views

Three mathematicians are forever in Prison

I'm excited to share the following riddle. It was given to me more than two years ago and I finally solved it last summer (after not thinking about it for a long time). In my desperation, I tried to ...
LFH's user avatar
  • 797
64 votes
4 answers
5k views

Gerrymandering Puzzle - Rig the Election

The following graphic is a map of the country Mathlandia: You are currently running for reelection, but the polls aren't exactly in your favor. Each square in this grid is a county. Counties with a ...
greenturtle3141's user avatar
62 votes
3 answers
7k views

Left coin, right coin, last coin?

In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put them on the table in front of them. Then each ...
GOTO 0's user avatar
  • 13.5k
62 votes
2 answers
9k views

It's getting harder and harder not to offend anyone

Andy, Bob and Chuck are old friends meeting for the first time in years. Scene 1: At the intersection ANDY: Hey guys! Long time no see! BOB: Hey, nice to see you, Andy! Have you seen Chuck? Is ...
Jafe's user avatar
  • 78k
61 votes
5 answers
5k views

Who shall come to the tea party?

All of your stuffed animals are assembled, anxiously waiting to learn who will be be invited as the Guest of Honor to your next tea party. This is to be an exclusive party, after all, as there is ...
Trevor Powell's user avatar
60 votes
4 answers
84k views

What is the maximum number of solutions a Sudoku puzzle can have?

I've seen Sudoku puzzles that can be solved two different ways. Referring to a traditional 9x9 grid: Is it possible for a Sudoku puzzle to have more than two solutions? If so, what is the maximum ...
WendiKidd's user avatar
  • 2,483
59 votes
4 answers
10k views

Interview Question or Pathbreaking puzzle

I thought this changes the way series of numbers are looked at 1 1 1 2 1 1 2 1 1 Write down the next three lines
skv's user avatar
  • 5,002
57 votes
10 answers
9k views

A well balanced puzzle: Logic puzzle(s) in visual disguise

This is a rather involved puzzle and might require a bit of stamina. All of the puzzle is in image form. The introduction text is not needed for the puzzle. At the end of the puzzle you'll get a short ...
BmyGuest's user avatar
  • 18.2k
56 votes
16 answers
12k views

How can I convince my colour blind friend that his two balls have different colours?

This question is inspired by this one, inspired by another Stack Exchange network question. My colour-blind friend has two balls, one red and one green. However, he is convinced that they are the ...
Kepotx's user avatar
  • 2,094
55 votes
8 answers
18k views

The Cucumber Paradox

Suppose you have 100 lbs of cucumbers and these cucumbers consist of 99% water. You decide to leave the cucumbers in the sun for a while until they consist of 98% water. You bring the cucumbers back ...
NL628's user avatar
  • 7,490
53 votes
4 answers
6k views

Is this chromatic puzzle always solvable?

I've created a new puzzle from an Alexey Nigin's idea. It consists of a 8x8 board where each square is randomly assigned one of three colors. A movement is defined by picking any two orthogonal ...
Edgar G.'s user avatar
  • 1,003
53 votes
3 answers
7k views

Sliding Bolt Puzzle

You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door. ...
diabonas's user avatar
  • 968
53 votes
2 answers
4k views

A Robot's Last Words

There, spread out all over the floor, were the mechanical pieces of a robot. Something had torn it apart, and the debris spanned a radius of a few meters. There was no sign of what might have caused ...
Tryth's user avatar
  • 14k
52 votes
11 answers
11k views

Turning a goat?

This is a goat made up of 5 sticks. You have to move (change position) any one stick of them such that its head turns to the right side (above the right leg). Notice currently its head is on the left ...
prog_SAHIL's user avatar
  • 5,353
52 votes
4 answers
6k views

Batman and the piano

Batman: Alfred. Are you there? Alfred: Yes, Master Bruce. How may I help you? Batman: ...
Khale_Kitha's user avatar
  • 8,442
52 votes
2 answers
6k views

A crossword so simple, it practically solves itself

An entry in the 19th fortnightly challenge... A Grid Some Clues There are three examples of this in the finished grid Two answers that touch a corner, in relation to 25A (D) Contained in the ...
Alconja's user avatar
  • 37.3k
50 votes
15 answers
7k views

Find the identity of the four troll brothers

The four troll brothers Wudhor, Xhaqan, Yijlob and Zrowag have the following properties: Wudhor always says the truth. Xhaqan always lies. Yijlob lies or says the truth unpredictably. ...
Lynn's user avatar
  • 916
50 votes
1 answer
3k views

Edward's Maze I

Edward's "revenge" on Bob the mute house servant Edward had enough! This was it! During the yearly sorcerer meet in a hidden cellar in Léon, Edward discovered a red stain on his precious robe. ...
Katai's user avatar
  • 1,163
49 votes
3 answers
5k views

Cover 63 squares of a chess board

Can you find 3 similar geometrical figures (common shape but can be different sizes) A, B and C with the following property: If you remove any square from a 8x8 chess board, then the remaining area ...
ThomasL's user avatar
  • 12.2k
49 votes
2 answers
4k views

Reverse Puzzling

George is a great puzzler, so I was extremely surprised when he didn't immediately know the answer to a really famous puzzle. It's a puzzle that you probably did years ago, and have heard so often ...
Dr Xorile's user avatar
  • 23.7k
49 votes
4 answers
16k views

I don't know the two numbers... but now I do

Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
durron597's user avatar
  • 2,374
49 votes
10 answers
5k views

Clever Jack - A logical fairy tale

As so often happens in fairy tales, there once was a king who had an intractable problem, one that even his wisest advisers could not solve. After many years of frustration, the exasperated king ...
crcroberts's user avatar
  • 1,833
48 votes
9 answers
23k views

IQ test question with diagonal lines in 3x1 grids

Can someone explain me the logic behind this? I think it is hard. The question is: What comes next in the pattern? (out of the 5 possibilities)
Ozkan's user avatar
  • 597
48 votes
11 answers
10k views

3 doors, three guards, one stone

You are in a room with three doors. Behind two of them, the darkest pit of hell waits for you to make a mistake. The other door leads to heaven and freedom. Each door is guarded by a guard: Michael, ...
Andrii Chumakov's user avatar
48 votes
3 answers
3k views

Tiling with T-tetrominos in gravity

The goal is to tile all the white squares using T-tetrominos when there is gravity pulling the tetrominos downwards like regular tetris. The black squares are void and the ground is just below the ...
Alexandros's user avatar
  • 1,137
47 votes
3 answers
3k views

Animal Cross(word)ing

An entry in Fortnightly Topic Challenge #43: Variety Crossword Grids Each of the 40 clues listed below (a mix of pop culture and science/nature) yields the name of an animal. Your task is to solve ...
Stiv's user avatar
  • 145k
47 votes
4 answers
10k views

The coolest checkerboard magic trick

In the small town of Terni (Italy), there's a couple of young friends named Marco and Leonardo, who like to perform magic tricks to a restricted audience of common friends and relatives. They like to ...
Marco Bonelli's user avatar
47 votes
2 answers
2k views

lolcatz can haz ur infinit cheeseboard

This is a problem on an infinite chessboard with pieces called lolcatz. They can move like queens or knightriders, but have a strange disadvantage... ... you've never heard of knightriders? Well, ...
deep thought's user avatar
  • 5,168
47 votes
5 answers
6k views

Who poisoned Hugh G. Pokitz? (a murder mystery logic puzzle)

Preface After your last mishap with a heap full of rabbits, you got sick of being lied to. Isn't life just so much easier when you can conclusively tell if someone's been telling the truth or not? ...
Bailey M's user avatar
  • 17k
46 votes
10 answers
23k views

Puzzle: Who hacked the computer?

I was working my way through some Knight and Knave Puzzles in Discrete Maths by Rosen, when I came across the following question: Four friends have been identified as suspects for an unauthorized ...
pranav's user avatar
  • 1,015
46 votes
1 answer
3k views

The Persistence Of Memory

You find yourself on the floor, slowly waking up and unable to remember how you got here. As you slowly come to your senses, you realize that another weird guy has trapped you in another unfamiliar ...
Deusovi's user avatar
  • 147k
45 votes
8 answers
9k views

Haters gonna hate

In a classroom, there are $20$ students and every student mutually hates exactly $3$ other students in the class. (If X hates Y, Y hates X as well.) The principal summons some of the students from ...
Oray's user avatar
  • 30.4k
45 votes
6 answers
8k views

Burning ropes as timers

You have 2 identical ropes which burn at a specific rate, and an unlimited supply of matches. When you light one end of a rope, the fire will take exactly 1 hour to travel to the other end of the rope....
Kendall Frey's user avatar
  • 3,393

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